(C) When the video is played in reverse,the time variable $t$ is replaced by $-t$. $1$. Position vector $\vec{r}(t)$ remains the same at the specific

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(C) When the video is played in reverse,the time variable $t$ is replaced by $-t$. $1$. Position vector $\vec{r}(t)$ remains the same at the specific moment $A$ because the object is at the same spatial location,so $\vec{r}_{obs} = \vec{r}$. $2$. Velocity is defined as $\vec{v} = \frac{d\vec{r}}{dt}$. In reverse,$\vec{v}_{obs} = \frac{d\vec{r}}{d(-t)} = -\frac{d\vec{r}}{dt} = -\vec{v}$. $3$. Acceleration is defined as $\vec{a} = \frac{d\vec{v}}{dt}$. In reverse,$\vec{a}_{obs} = \frac{d(\vec{v}_{obs})}{d(-t)} = \frac{d(-\vec{v})}{-dt} = \frac{d\vec{v}}{dt} = \vec{a}$. Thus,the observed values are $\vec{r}, -\vec{v}, \vec{a}$.

Class 11 Physics Motion in Straight Line Mix Examples-Motion in Straight Line

Difficult

$A$ charged object is launched inside a time-varying electric field. Its motion is recorded by a video camera on a video tape. When it is at a certain moment $A$,its position vector $\vec{r}$,velocity $\vec{v}$,and acceleration $\vec{a}$ are measured. $A$ student watches the video at a later time but mistakenly plays the tape in the reverse direction. What are the position,velocity,and acceleration of the object at moment $A$ observed by the student,respectively?

A
$\vec{r}, \vec{v}, \vec{a}$
B
$-\vec{r}, -\vec{v}, -\vec{a}$
C
$\vec{r}, -\vec{v}, \vec{a}$
D
$\vec{r}, \vec{v}, -\vec{a}$

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Motion in Straight Line

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Mix Examples-Motion in Straight Line

The figure shows the velocity $(v)$ of a particle plotted against time $(t)$.

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$A$ bogie of a uniformly moving train is suddenly detached from the train and stops after covering some distance. What is the relation between the distance covered by the bogie and the distance covered by the train in the same time?

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$A$ train starts from rest from a station with acceleration $0.2 \, m/s^2$ on a straight track and then comes to rest after attaining maximum speed at another station due to retardation $0.4 \, m/s^2$. If the total time spent is half an hour,then the distance between the two stations is [Neglect the length of the train]. (in $, km$)

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$A$ street car moves rectilinearly from station $A$ to the next station $B$ with an acceleration varying according to the law $a = (b - cx)$,where $b$ and $c$ are constants and $x$ is the distance from station $A$. The distance between the two stations and the maximum velocity are:

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Read each statement below carefully and state with reasons and examples,if it is true or false for a particle in one-dimensional motion:
$(a)$ With zero speed at an instant may have non-zero acceleration at that instant.
$(b)$ With zero speed may have non-zero velocity.
$(c)$ With constant speed must have zero acceleration.
$(d)$ With positive value of acceleration must be speeding up.

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The figure shows the velocity $(v)$ of a particle plotted against time $(t)$.

$A$ bogie of a uniformly moving train is suddenly detached from the train and stops after covering some distance. What is the relation between the distance covered by the bogie and the distance covered by the train in the same time?

$A$ street car moves rectilinearly from station $A$ to the next station $B$ with an acceleration varying according to the law $a = (b - cx)$,where $b$ and $c$ are constants and $x$ is the distance from station $A$. The distance between the two stations and the maximum velocity are:

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